When Worlds Collide: Different Comparative Static Predictions of Continuous and Discrete Agent Models with Land

Berliant, Marcus and Sabarwal, Tarun (2008): When Worlds Collide: Different Comparative Static Predictions of Continuous and Discrete Agent Models with Land.

Abstract

This paper presents a difference in the comparative statics of general equilibrium models with land when there are finitely many agents, and when there is a continuum of agents. Restricting attention to quasi-linear and Cobb-Douglas utility, it is shown that with finitely many agents, an increase in the (marginal) commuting cost increases land rent per unit (that is, land rent averaged over the consumer's equilibrium parcel) paid by the consumer located at each fixed distance from the central business district. In contrast, with a continuum of agents, average land rent goes up for consumers at each fixed distance close to the central business district, is constant at some intermediate distance, and decreases for locations farther away. Therefore, there is a qualitative difference between the two types of models, and this difference is potentially testable.

• Item Type: MPRA Paper
• Language: English
• Keywords: Large Urban Economies, Comparative Statics, Continuous and Discrete Agent Models
• Subjects: R - Urban, Rural, Regional, Real Estate, and Transportation Economics > R1 - General Regional Economics > R13 - General Equilibrium and Welfare Economic Analysis of Regional Economies; D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D51 - Exchange and Production Economies; R - Urban, Rural, Regional, Real Estate, and Transportation Economics > R1 - General Regional Economics > R14 - Land Use Patterns

References

Asami, Y., Fujita, M., Smith, T., 1991. On the foundations of land use theory: discrete versus continuous populations. Regional Science and Urban Economics 20, 473-508. Berliant, M., 1985. Equilibrium models with land: a criticism and an alternative. Regional Science and Urban Economics 15, 325-340. Berliant, M., 1991. Comments on "On the foundations of land use theory: discrete versus continuous populations" by Y. Asami, M. Fujita and T. Smith. Regional Science and Urban Economics 21, 639-45. Berliant, M., Fujita, M., 1992. Alonso's discrete population model of land use: efficient allocations and competitive equilibria. International Economic Review 33, 535-566. Berliant, M., LaFountain, C., 2006. Space in general equilibrium. In: Arnott, R., McMillen, D. (Eds.). A Companion to Urban Economics. Williston, VT: Blackwell, 109-127. Berliant, M., ten Raa, T., 1991. On the continuum approach of spatial and some local public goods or product differentiation models: some problems. Journal of Economic Theory 55, 95-120. Fujita, M., 1989. Urban Economic Theory. Cambridge: Cambridge University Press. Fujita, M., Thisse, J.-F., 2002. Economics of Agglomeration. Cambridge: Cambridge University Press. Kamecke, U., 1993. Mean city: a consistent approximation of bid rent equilibria. Journal of Urban Economics 33, 48-67. Lucas, R.E., Jr., Rossi-Hansberg, E., 2002. On the internal structure of cities. Econometrica 70, 1445-1476. McLean, R., Muench, T., 1981. Approximate decentralization of the Beckmann-Koopmans assignment/shipping problem for a large discrete Mills city and its limit relationship to the continuum Mills city. Cowles Foundation Working Paper No. 236. McMillen, D.P., McDonald, J.F., 2004. Reaction of house prices to a new rapid transit line: Chicago's midway line, 1983-1999. Real Estate Economics 32, 463-486. Papageorgiou, Y.Y., Pines, D., 1990. The logical foundations of urban economics are consistent. Journal of Economic Theory 50, 37-53.